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added random walk example

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mhjensen
2018-05-29 11:08:41 -04:00
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commit d34d39836b
8 changed files with 608 additions and 101 deletions
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doc/pub/How2ReadData/html/How2ReadData-reveal.html
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@@ -150,15 +150,7 @@ MathJax.Hub.Config({
<p>&nbsp;<br>
<center><h4>May 29, 2018</h4></center> <!-- date -->
<br>
<p>
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
</center>
</section>
<section>
<h2 id="___sec0">Introduction </h2>
<p>
@@ -198,10 +190,7 @@ tensorflow (see below for links etc). Moreover, the examples we
introduce will serve as inputs to many of our discussions later, as
well as allowing you to set up models and produce your own data and
get started with programming.
</section>
<section>
<h2 id="___sec1">Software and needed installations </h2>
<p>
@@ -246,10 +235,7 @@ you can use <b>pip</b> as well and simply install Python as
<p>
etc etc.
</section>
<section>
<h2 id="___sec2">Python installers </h2>
<p>
@@ -278,10 +264,7 @@ is a Python
distribution for scientific and analytic computing distribution and
analysis environment, available for free and under a commercial
license.
</section>
<section>
<h2 id="___sec3">Installing R, C++, cython or Julia </h2>
<p>
@@ -299,10 +282,7 @@ texts.
<p>
To install <b>R</b> with Jupyter notebook
<a href="https://mpacer.org/maths/r-kernel-for-ipython-notebook" target="_blank">follow the link here</a>
</section>
<section>
<h2 id="___sec4">Installing R, C++, cython, Numba etc </h2>
<p>
@@ -336,10 +316,7 @@ And to add more versatility, the Python package <a href="http://www.sympy.org/en
Finally, if you wish to use the light mark-up language
<a href="https://github.com/hplgit/doconce" target="_blank">doconce</a> you can convert a standard ascii text file into various HTML
formats, ipython notebooks, latex files, pdf files etc with minimal edits.
</section>
<section>
<h2 id="___sec5">Simple linear regression model using <b>scikit-learn</b> </h2>
<p>
@@ -644,10 +621,7 @@ plt.show()
</pre></div>
<p>
Similarly, using <b>R</b>, we can perform similar studies. The following <b>R</b> code illustrates this.
</section>
<section>
<h2 id="___sec6">Non-Linear Least squares in R </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
@@ -695,10 +669,7 @@ data = {<span style="color: #CD5555">&#39;Name&#39;</span>: [<span style="color:
data_pandas = pd.DataFrame(data)
display(data_pandas)
</pre></div>
</section>
<section>
<h2 id="___sec7">Examples </h2>
<p>
@@ -1396,6 +1367,107 @@ plt.axis([-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">5
plt.grid(<span style="color: #658b00">True</span>)
plt.show()
</pre></div>
<h3 id="___sec12">Random walk model </h3>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> PolynomialFeatures
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
steps=<span style="color: #B452CD">250</span>
distance=<span style="color: #B452CD">0</span>
x=<span style="color: #B452CD">0</span>
distance_list=[]
steps_list=[]
<span style="color: #8B008B; font-weight: bold">while</span> x&lt;steps:
distance+=np.random.randint(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">2</span>)
distance_list.append(distance)
x+=<span style="color: #B452CD">1</span>
steps_list.append(x)
plt.plot(steps_list,distance_list, color=<span style="color: #CD5555">&#39;green&#39;</span>, label=<span style="color: #CD5555">&quot;Random Walk Data&quot;</span>)
steps_list=np.asarray(steps_list)
distance_list=np.asarray(distance_list)
X=steps_list[:,np.newaxis]
<span style="color: #228B22">#Polynomial fits</span>
<span style="color: #228B22">#Degree 2</span>
poly_features=PolynomialFeatures(degree=<span style="color: #B452CD">2</span>, include_bias=<span style="color: #658b00">False</span>)
X_poly=poly_features.fit_transform(X)
lin_reg=LinearRegression()
poly_fit=lin_reg.fit(X_poly,distance_list)
b=lin_reg.coef_
c=lin_reg.intercept_
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;2nd degree coefficients:&quot;</span>)
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;zero power: &quot;</span>,c)
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;first power: &quot;</span>, b[<span style="color: #B452CD">0</span>])
<span style="color: #8B008B; font-weight: bold">print</span> (<span style="color: #CD5555">&quot;second power: &quot;</span>,b[<span style="color: #B452CD">1</span>])
z = np.arange(<span style="color: #B452CD">0</span>, steps, .<span style="color: #B452CD">01</span>)
z_mod=b[<span style="color: #B452CD">1</span>]*z**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*z+c
fit_mod=b[<span style="color: #B452CD">1</span>]*X**<span style="color: #B452CD">2</span>+b[<span style="color: #B452CD">0</span>]*X+c
plt.plot(z, z_mod, color=<span style="color: #CD5555">&#39;r&#39;</span>, label=<span style="color: #CD5555">&quot;2nd Degree Fit&quot;</span>)
plt.title(<span style="color: #CD5555">&quot;Polynomial Regression&quot;</span>)
plt.xlabel(<span style="color: #CD5555">&quot;Steps&quot;</span>)
plt.ylabel(<span style="color: #CD5555">&quot;Distance&quot;</span>)
<span style="color: #228B22">#Degree 10</span>
poly_features10=PolynomialFeatures(degree=<span style="color: #B452CD">10</span>, include_bias=<span style="color: #658b00">False</span>)
X_poly10=poly_features10.fit_transform(X)
poly_fit10=lin_reg.fit(X_poly10,distance_list)
y_plot=poly_fit10.predict(X_poly10)
plt.plot(X, y_plot, color=<span style="color: #CD5555">&#39;black&#39;</span>, label=<span style="color: #CD5555">&quot;10th Degree Fit&quot;</span>)
plt.legend()
plt.show()
<span style="color: #228B22">#Decision Tree Regression</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">2</span>)
regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
regr_3=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
regr_1.fit(X, distance_list)
regr_2.fit(X, distance_list)
regr_3.fit(X, distance_list)
X_test = np.arange(<span style="color: #B452CD">0.0</span>, steps, <span style="color: #B452CD">0.01</span>)[:, np.newaxis]
y_1 = regr_1.predict(X_test)
y_2 = regr_2.predict(X_test)
y_3=regr_3.predict(X_test)
<span style="color: #228B22"># Plot the results</span>
plt.figure()
plt.scatter(X, distance_list, s=<span style="color: #B452CD">2.5</span>, c=<span style="color: #CD5555">&quot;black&quot;</span>, label=<span style="color: #CD5555">&quot;data&quot;</span>)
plt.plot(X_test, y_1, color=<span style="color: #CD5555">&quot;red&quot;</span>,
label=<span style="color: #CD5555">&quot;max_depth=2&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.plot(X_test, y_2, color=<span style="color: #CD5555">&quot;green&quot;</span>, label=<span style="color: #CD5555">&quot;max_depth=5&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.plot(X_test, y_3, color=<span style="color: #CD5555">&quot;m&quot;</span>, label=<span style="color: #CD5555">&quot;max_depth=7&quot;</span>, linewidth=<span style="color: #B452CD">2</span>)
plt.xlabel(<span style="color: #CD5555">&quot;Data&quot;</span>)
plt.ylabel(<span style="color: #CD5555">&quot;Darget&quot;</span>)
plt.title(<span style="color: #CD5555">&quot;Decision Tree Regression&quot;</span>)
plt.legend()
plt.show()
</pre></div>
<p>
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
</center>
</section>